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A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations. (English) Zbl 1244.65099
Summary: A shifted Jacobi-Gauss collocation spectral method is proposed for solving the nonlinear Lane-Emden type equation. The spatial approximation is based on shifted Jacobi polynomials P T,n (α,β) (x) with α,β(-1,),T>0, and n is the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. The method is easy to implement and yields very accurate results.
MSC:
65L05Initial value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34A34Nonlinear ODE and systems, general
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